AKA, put the name of the site in the password :)

Not necessarily, but just a pattern that only you would likely remember.

You need a pattern that only you recognise/understand, not just remember. It takes only one leak of your password from service FooBar that looks like "f....b" to know what to try on other sites. Patterns easy to remember are mostly easy to understand.

With LLM that sort of approach can be attacked at scale

"MyPasswordIsSecureDespiteNotBeingComplexBecauseItIsLong_BobsForum" is great until Bob's Forum gets hacked and it turns out that they were storing your password in plain text and your password of "MyPasswordIsSecureDespiteNotBeingComplexBecauseItIsLong_Google" becomes easily guessed.

One way to mitigate such a problem is to use the hash of this text as the password, instead of using the text directly.

That algorithm becomes analogous to the password to your password manager.